Question

Two vertices of a triangle are A (1, 1), B (2, –3). If its centroid is (2, 1) find the third vertex.

Answer 1

Let the co-ordinates of the third vertex be (x, y). Then, 

Co-ordinates of the centroid are \(\bigg(\frac{1+2+x}{3},\frac{1-3+y}{3}\bigg)\) = \(\bigg(\frac{3+x}{3},\frac{-2+y}{3}\bigg)\)

Given, \(\bigg(\frac{3+x}{3},\frac{-2+y}{3}\bigg)\) = (2.1)

⇒ \(\frac{3+x}{3} = 2\) and \(\frac{-2+y}{3} = 1\)

⇒ 3 + x = 6 and – 2 + y = 3 

⇒ x = 3 and y = 5 

∴ Co-ordinates of the third vertex are (3, 5).